X-ray crystallography is a method of determining the arrangement of atoms within a crystal, in which a beam of X-rays strikes a crystal and scatters into many different directions. From the angles and intensities of these scattered beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their disorder and sundry other information.
Since very many materials can form crystals—such as salts, metals, minerals, semiconductors, as well as various inorganic, organic and biological molecules—X-ray crystallography has been fundamental in the development of many scientific fields. In its first decades of use, this method determined the size of atoms, the lengths and types of chemical bonds, and the atomic-scale differences among various materials, especially minerals and alloys. The method also revealed the structure and functioning of many biological molecules, including vitamins, drugs, proteins and nucleic acids such as DNA. X-ray crystallography is still a chief method for characterizing the atomic structure of new materials and in discerning materials that appear similar by other experiments. X-ray crystal structures can also account for unusual electronic or elastic properties of a material, shed light on chemical interactions and processes, or serve as the basis for designing pharmaceuticals against diseases.
Crystals are regular arrays of atoms, and X-rays can be considered waves of electromagnetic radiation. Atoms scatter X-ray waves, primarily through the atoms' electrons. Just as an ocean wave striking a lighthouse produces secondary circular waves emanating from the lighthouse, so an X-ray striking an electron produces secondary spherical waves emanating from the electron. This phenomenon is known as scattering, and the electron is known as the scatterer. A regular array of scatterers produces a regular array of spherical waves. Although these waves cancel one another out in most directions (destructive interference), they add constructively in a few specific directions, determined by Bragg's law, 2d sin θ=nλ, where n is any integer. These specific directions appear as spots on the diffraction pattern, often called reflections. Thus, X-ray diffraction results from an electromagnetic wave (the X-ray) impinging on a regular array of scatterers, the repeating arrangement of atoms within the crystal.
X-rays are used to produce the diffraction pattern because their wavelength λ is typically the same order of magnitude (1-100 Ångströms) as the spacing d between planes in the crystal. In principle, any wave impinging on a regular array of scatterers produces diffraction. To produce significant diffraction, the spacing between the scatterers and the wavelength of the impinging wave should be roughly similar in size.
The idea that crystals could be used as a diffraction grating for X-rays arose in 1912 in a conversation between Paul Peter Ewald and Max von Laue in the English Garden in Munich. Ewald had proposed a resonator model of crystals for his thesis, but this model could not be validated using visible light, since the wavelength was much larger than the spacing between the resonators. Von Laue realized that electromagnetic radiation of a shorter wavelength was needed to observe such small spacings, and suggested that X-rays might have a wavelength comparable to the unit-cell spacing in crystals. Von Laue worked with two technicians, Walter Friedrich and his assistant Paul Knipping, to shine a beam of X-rays through a sphalerite crystal and record its diffraction on a photographic plate. After being developed, the plate showed a large number of well-defined spots arranged in a pattern of intersecting circles around the spot produced by the central beam, now referred to as a Laue image. Von Laue developed a mathematical relationship that connects the scattering angles and the size and orientation of the unit-cell spacings in the crystal.
In a typical X-ray crystallography system, after a crystal specimen has been obtained, the specimen is mounted on a goniometer and gradually rotated while being bombarded with X-rays, producing a diffraction pattern, or oscillation (or rotation) image of regularly spaced known spots. The two-dimensional images taken at different rotations are converted into a three-dimensional model of the density of electrons within the crystal using the mathematical method of Fourier transforms, and combined with chemical data known for the sample. Poor resolution or even errors may result if the crystals are too small, or not uniform enough in their internal makeup.
X-ray crystallography is related to several other methods for determining atomic structures. Similar diffraction patterns can be produced by scattering electrons or neutrons, which are likewise interpreted using a Fourier transform. If single crystals of sufficient size cannot be obtained, various X-ray scattering methods can be applied to obtain less detailed information.
There are two ways of performing X-ray crystallography using Laue images. In transmission Laue systems, the film or X-ray detector is placed behind the crystal specimen to record X-ray beams which are transmitted through the crystal. In back-reflection Laue systems, also generally referred to herein as “back-reflection X-ray detectors”, the actual film or X-ray detector is placed between the X-ray source and the crystal specimen. Thus, the X-ray beams which are diffracted in a backwards direction are recorded.
Therefore, in a back-reflection X-ray detector, the X-ray source is on the same side of the specimen as the film or detector onto which the Laue images are reflected. This arrangement provides for a compact size relative to a transmission X-ray detector system. Back-reflection geometry is also the only universal method for thick samples of more than a mm thickness, such as boules of silicon, turbine blades, etc which are too thick to penetrate with 10 to 30 keV x-rays.
Back-reflection X-ray crystallography has recently increased in importance in manufacturing, particularly in the area of electronic devices incorporating thin crystals, for example in laser optical devices, such as CD or DVD players, and the like. It is very important in the manufacturing environment that X-ray detectors be able to quickly and automatically obtain and analyze Laue images to determine, for example, optimal specimen orientation for industrial applications of the specimen. The relatively compact nature of a back-reflection X-ray detector renders it suitable to numerous manufacturing applications.
The Multiwire Laboratories MWL110™ X-ray detector is an example of an X-ray detector which quickly collects a back-reflection Laue image for analysis. The Laue image typically contains 6 to 30 spots that, if properly analyzed, will tell how the rows and columns of atoms lined up in the crystal are oriented with respect to the X-ray beam that creates the image. This is usually the information the user is looking for, so as to enable sample rotation using a two or three axis rotation stage, or goniometer, to bring the sample into proper alignment for the application at hand.
In typical usage, the Laue spots are “indexed” or named with three integer numbers called “Miller indices”, which describes the fixed angular relationship between the planes. The information needed is contained in a mathematical 3 by 3 matrix called the Orientation Matrix. The Orientation Matrix provides a complete description of the unit cell of the crystal in question as well as its angular alignment with respect to the x-ray beam.
Several difficulties have arisen in the typical usage of back-reflection X-ray crystallography, some of which are referred to here.
Determination of the Miller index tends to be sensitive to measurement of the angle between spots on a Laue image, which, in turn is sensitive to the “film-to-specimen” distance. In a typical application, the film-to-specimen distance ranges from 125 mm to 175 mm. If the specimen is not over the center of the rotary stage of the goniometer, this distance can easily change by a few mm during sample rotation. If the film-to-specimen distance is off by a couple of mm, then the measurement of the angle, for example say 10 degrees, between two spots will be off, complicating the generation of Miller indexing of the spots. Thus, the user would have to know enough crystallography to judge if the resulting Miller index is correct or not.
Next, typical X-ray detectors require a user to identify points on the Laue image to identify the center of spots. Typically, the user had to manually select all the spots to be indexed in the Laue image, and the first two spots selected had to be in an “indexing table”. Thus, there is a need for an X-ray detector to automatically detect the center of spots on a Laue image.
Also, in prior art X-ray detectors, the user had to index 100% of the points selected. If there was a “bad” point, for example, one with a higher Miller index than allowed by the MaxHKL setting, or “noise”, etc., then expert intervention would normally be required to operate the detector. The expert would typically need to be very knowledgeable about crystallography and experienced in indexing a Laue image. This is not a desirable situation, particularly in a manufacturing environment. Thus, there is a need for an X-ray detection system that can automatically tolerate such bad points and still arrive at the correct answer by ignoring a small fraction of the “bad” points.
In prior art X-ray detection systems, the user could typically spend significant time manually selecting spots by hand before finding those which were in an indexing table. Thus, there is a need for a system that automatically cycles through all the various possible combinations of spots, determining all possible orientation matrices and select those with the lowest average Miller index.
Additionally, X-ray detectors to date have fitted the orientation matrix to just the first two points selected. Thus, there is a need for a detector that automatically fits the orientation matrix to all the Laue image data points, not just the first two points that were used to create the orientation matrix. This would allow for a more accurate orientation matrix than if it were built only from the first two points selected by the user.
There is also a need for an X-ray detector that provides for creation of “macros”, or pre-determined sequences of steps which automate entire sequences of collecting Laue images, finding spots, generating Miller indices, and determining orientation. These macros would be particularly useful in manufacturing environments.
It would also be useful for an X-ray detector to allow the user to specify and highlight additional planes of interest, even if they are behind the collimator, and thus not “seen” by the detector.
In prior X-ray detectors, a single maximum value could typically be provided for the planes H, K and L. In cases where the “unit cell” vectors differ greatly in length, such as with quartz, where the c-axis is about twice the length of the a-axis, there is a need for an X-ray detector that allows three independent maximal values for H, K and L, such as Hmax, Kmax and Lmax.
Typical X-ray detectors allow Miller indexing of only one or, at most, very few planes. Thus, it is desirable to provide an X-ray detector that allows for indexing all the visible planes in the image, even for those having high Miller index, for example, planes indices that vary from 0-15.
Also, for rhombohedral unit cells, those in which a=b=c, alpha=beta=gamma, and which are not 90 degrees, e.g., 56.3 degrees, there is a need for an X-ray detector which indexes in rhombohedral coordinates, but displays in hexagonal coordinates. This feature would result in more positive indexing as transformation converts the rhombohedral HKLs into Hexagonal form that humans understand more readily. The indexing in rhombohedral coordinates is more reliable because the Miller indices are lower than in the hexagonal case.